Lewis and Counterfactuals

Introduction
Counterfactuals are subjunctive conditionals which take the form If x Then y and where the antecedent (x) is presumed false in the actual world (Starr, 2022, pp1). Counterfactuals are very intuitive and used in everyday life. For example, after a close encounter with a candle a parent may have warned you ‘‘If you had put your hair any closer to the flamee1, then your hair would have been burnte2’. This commonly used counterfactual seems true and presumes a dependency between e1 and e2 so that if the antecedent had occurred in this world, then the consequence would occur. The Counterfactual Theory of Causation attempts to understand causation in terms of this dependency between events (Menzies, Beebee, 2020, p1).  

​There have been several attempts at providing a satisfactory analysis of counterfactuals, but the most prominent analysis is from Davie Lewis (Lewis, 1979, pp.455-476). This essay will first assess Lewis's analysis of counterfactuals and how it avoids certain issues. Then I will present one of its hardest objections, namely indeterminism, and critique Lewis’s response. A successfully defended analysis of counterfactuals can defend itself from any major objection. I believe Lewis's analysis of counterfactuals is unconvincing as a probabilistic or indeterministic world leads to many intuitively true counterfactuals to be false therefore he does not provide a successfully defended analysis.

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Lewis’s analysis of counterfactuals
Lewis’s Analysis of Counterfactuals goes as follows: “If it were that A, then it would be that C is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall than is any world where A is true but C is false” (Lewis, 1979, p465). Or put another way, a counterfactual is true if and only if the consequent is true in the possible world that most resembles our current world and where the antecedent is true. For example, “If you had put your hand in the fire e1, then it would have been warm e2”. This counterfactual is true if and only if the possible world which is most similar to our actual world is a world where I put my hand in the firee1 and my hand begins to warme2. The counterfactual is false if the most similar world to our own is where the antecedent does not have the consequent of a warm hand. Lewis's analysis appeals to a possible world systematic for the truth values of counterfactuals.

Lewis notes that this analysis is ‘extremely vague’ but counts that as a ‘virtue’ (Lewis, 1979, p.465). We have not yet given a similarity weighting to distinguish the closest world to our own, but without an exact measure of similarity between worlds, we can see the strength of his analysis. When we state a counterfactual is true, we are proposing a state of the world which is similar to ours where the antecedent is true and then proposing the outcome would lead to a certain consequence. To take the example above, most would intuitively believe that if the world was different and you decided to put your hand in the fire after all, then it is true that your hand would warm. This is because a world similar to ours, i.e. where fire has the same properties and you exist, where the antecedent is true seems to lead to the consequence of the warm hand. Lewis's analysis shows the intuitiveness of counterfactuals using similar possible worlds and provides a plausible account to assess the truth of counterfactuals and dependency between events.

 

The Future similarity objection
Lewis’s analysis is intuitive in many examples however Kit Fine presents an objection against Lewis’s appeal to the similarities of possible worlds as it leads to some very counterintuitive examples (Lewis, 1979, p467). Fine argues that the counterfactual “If Nixon had pressed the button, there would have been a nuclear holocaust” is very intuitive and seems very true to say. However, Fine argues that following Lewis’s analysis the most similar world to ours where the antecedent is true, is where Nixon presses the button and there isn’t a nuclear holocaust. The antecedent could be true and the consequence false if there was a second minor change, such as a malfunction with the signal. The nuclear holocaust is obviously a great deviation from our current world as a world with half its cities obliterated is far less similar than a world which has its cities and population intact. Therefore, the Nixon counterfactual is false according to Lewis’s analysis. Similar counterfactuals such as if Einstein had not been born then general relativity would have not been discovered in the 1920s also suffer the same objection since the most similar world would include another scientist having a similar history as Einstein and discovering it. Consequently, Lewis’s analysis of counterfactuals leads to absurd and counterintuitive cases where common counterfactuals are false. Unless we are willing to grant counterfactuals like the Nixion one is false Lewis can’t motivate or defend his analysis.

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Lewis’s Similarity Rebuttal
On the other hand, Lewis argues that the similarity between possible worlds is not as clear as an approximate future match or finding a world which resembles the current world now but rather similarity to other worlds is context-specific and the weighting requires considering facts and laws of our world (Lewis, 1979, pp467-472). Lewis demonstrates this by imagining a world which could be ours, ‘w0’, where Nixon does not press the button and there is no nuclear holocaust. In w0 it is presumed that if Nixon had pressed the button, the system the button is attached to would be ‘faultless’. He then compares w0 to 4 other possible worlds. For brevity, I will only assess two worlds which will demonstrate that Fine's counterfactual would be true on Lewis’s analysis and then present his similarity weighting.

Similarity in Fine’s counterfactual
Lewis presents a possible world, w1, which is identical to w0 just before the antecedent is true but diverts just before into w1 to make the antecedent true. (Lewis, 1979, p469). Before Nixon decides not to press the button in w0, there is a miracle, such as a change in thought, which leads to Nixon pressing the button. No further miracles occur afterwards, and Fines counterfactual is correct in w1.

Lewis then compares a second possible world, ‘w3’, which is identical to our world just before Nixion presses the button, but diverges, due to a small miracle, to a world where Nixion presses the button (Lewis, 1979, p470). However, shortly after the button is pressed another miracle such as the wire snapping leads to the nuclear holocaust not occurring. It might seem, as Fine argues, that w3 is a more similar world as both w3 and w0 don’t have a future with a nuclear holocaust. On the other hand, if after pressing the button the consequence is false, Lewis argues there is still a great divergence from w0 as Nixon's actions ‘Left its mark’. For example, the humidity in the room will have increased due to more stress, different thoughts and emotions will be going through the civil servant's mind who are watching etc. Furthermore, there will be greater long-term effects such as Nixion's approach to political issues might change and be more confident in pressing the button again. Perhaps news of this occurring will make the USSR more likely to attack etc. Consequently, although w3 future is approximately similar with regards to no nuclear holocaust occurring immediately after the event, there is still a great deviation long term. To gain a perfect match after the event of pushing the button, all of those consequences, like people seeing him press the button, the kinetic energy released etc. would have to be covered up with many miracles. A world with many miracles occurring is less similar to our world. Therefore, Fine's objection is false, and Lewis's analysis would conclude that the Nixon counterfactual is true.

Lewis’s Similarity Weighting 
From this and analysing other worlds Lewis presents a similarity weighting which saves his analysis from Fine’s objection and gives a clearer philosophical analysis for assessing the similarity between possible worlds. It can be summarised as follows:

The first and most important principle in assessing the similarity of worlds is avoiding ‘big, widespread, diverse violation of laws’(Lewis, 1979, pp468-472). This is to say that the laws which hold in our world also hold in a similar world are not violated on a large scale. Some violation of law may be necessary for the antecedent to be true but widespread miracles, like afterwards in the Nixon case, must be avoided. A world will lots of violations of law or miracles is less similar to our world which hardly has any miracles therefore, a possible world with lots of miracles is less similar. 

The second most important principle is to ‘maximize the spatiotemporal region throughout which perfect match of particular facts prevails’(Lewis, 1979, pp468-472). This is to say that the history of the most similar world should be as close as possible to the actual world. If the world was deterministic without any miracles, then the whole of history would be different to lead Nixion to press the button. A world with a different history could be drastically different to our own therefore, the history of a similar world must be as close to ours as possible which can be achieved with a small violation of law to allow the antecedent to be true.  As this principle is second, history can be maximised before the antecedent is true but not after since this would lead to widespread violations of laws.

The third principle in the similarity weighting is to avoid ‘small, localised, simple violations of law’ (Lewis, 1979, pp468-472). Meaning, that although a small violation of law might be necessary for the antecedent to be true, we should avoid any more than is necessary. Lastly, ‘Approximate match’ is of hardly any importance. This is to say that an approximate match such as both worlds not having a nuclear holocaust is of little importance since the above principles are more important when assessing similarity of worlds.

As a result, Lewis presents a strong defence of his analysis of counterfactuals with a very intuitive similarity weighting which is simple. The intuitiveness and simplicity are a great strength of Lewis's analysis and successfully rebuttals Fine's future similarity objection.

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Indeterminism objection
Lewis’s similarity weighting prioritises widespread violations of Laws first which prevents Fines type of future similarity objection. However, we can strengthen Fine's objection with an indeterminism or probabilistic world which allows the possibility of a widespread cover-up and perfect future match without violation of laws (Edgington, 2004, p14). Therefore, Lewis's analysis and similarity weighting of counterfactuals are not defendable against Fine’s counterfactual.

For example, presume indeterminist so that the laws and facts about our world are highly probable to be a certain way (Edgington, 2004, p14). Nevertheless, since the world is indeterministic there may be a very low possibility that they become false. Consequently, there is a possibility, say 0.001, that when Nixon presses the button nothing will happen and that all the consequences of Nixon pressing the button diminish so that, without any violation of laws, we get perfect match. Of course, such a possibility is highly unlikely but using Lewis similarity weighting there is a similar possible world where the antecedent is true and consequent false which doesn’t have widespread violations of laws. Such a world has a perfect match before and then after the button is pressed. This possible world would be the closest possible world on Lewis’s account so the counterfactual if Nixon pressed the button, then there would be a nuclear holocaust is overtly false. This shows that in an indeterministic world, intuitive and common counterfactuals like the one above are false. Consequently, Lewis’s analysis does not capture the truth of counterfactuals and does not present a successful defence of his analysis.

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Quasi-miracles Rebuttal
Lewis attempts to use a miracle analogy to defend his similarity weighting (Lewis, 1986), p.59). He argues that although in an indeterministic world perfect cover-ups are conceivable without law violation, Lewis argues that such events are ‘remarkable coincidences’ which can be considered as a miracle. Counterfactuals like ‘if Nixon pressed the button, then nothing would happen’ are similar to remarkable events such as finding long lost trencher by throwing a dart at a map and digging where it lands. Although entirely possible if the dart has an equal chance of landing anywhere on the map. It is still highly remarkable that treasure is found. Consequently, we ought to prefer possible worlds which do not contain quasi-miracles over more probable ones, for the same reasons we wouldn’t think a possible world which contains real miracles is a similar world to ours to one which does not have real miracles. Therefore, Lewis argues his analysis of counterfactuals is not greatly damaged by indeterminism as improbable indeterministic events are similar to miracles which are law violations.

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Objections to quasi-miracles 
At first, Lewis's argument seems very plausible as quasi-miracles seem like the last things to occur and therefore a world with them is less similar to ours. However, I believe this is not true for three reasons.

First, if quasi-miracles are understood as highly improbable facts, I believe one of the greatest examples of a quasi-miracle is you reading this essay. For you to be here reading this essay our planet would have to have been able to sustain life, unlike most of the planets in our universe. Second, an incredibly long unbroken chain of events where your ancestors survived long enough to reproduce would have had to take place. Third, all the influences in your life would have had to take place to bring you here now reading this paper. At any point in an indeterministic universe, one of these facts could have been different which would have changed the events of now. Our existence seems like a remarkable coincidence and yet we exist in this world. This is simplified but it seems to me that quasi-miracles should not be a disqualifier for the similarity between worlds as it seems they take place quite often.

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Second, at what point does a quasi-miracle stop being a remarkable coincidence since it could be the case that something is less probable but still quite possible. For example, Nixon pressing the button could have a 0.01 chance of a complete cover-up. This weakens the appeal to quasi-miracles since if Nixon pressed the button 100 times one of those times would lead to a coverup.

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Third, there are counterfactual statements which seem to suggest that a world with quasi-miracles is more probable than a possible world without them (Dodd, 2011, pp353). For example, imagine a six-sided dice and the counterfactual 1) If I had rolled the dice a thousand times then it would have not landed on the same number every time. This counterfactual seems true since if it did land on one number every time then it would seem like a ‘remarkable coincidence’ and according to Lewis, we should not assess worlds with quasi miracles as a more similar world. However, someone else might give the counterfactual 2) if I had rolled the dice a thousand times then it would have landed x (where x is a mixed sequence of possible numbers the dice could land on). This counterfactual is less remarkable than if the dice landed on one number every time since common experience often sees a random different pattern of dice roles. A casino player would not suspect any foul play if after rolling the dice in 1000 games the dice landed on a random sequence of numbers. Only if the dice landed on six every game would a player suspect cheating and demand a refund. However, counterfactual 1) has a 1/6 ^999 chance of happening. But counterfactual 2) has a 1/6^1000 chance of happening. Even though it seems less remarkable to see a particular random series of numbers from a dice roll, any specific random series is less probable than the dice landing on the same number every time. If Lewis’s quasi-miracle was correct more probable worlds would be treated as a violation of law and a less probable would be favoured. This is absurd. Consequently, I do not believe Lewis’ defence is successful.

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Best System Analysis of Laws
After showing that Quasi-miracles are untenable, I believe Lewis's best defence of his analysis is appealing to a Humean view of laws, specifically, the Best System of analysis of Laws (Lewis, 1994, pp480). If laws must fit the best system of analysis (BSA), then a cover-up may be a violation of laws (Noordhof, 2023, slide 31). As a result, although they seem possible, they are still a type of law violation on the best system analysis of laws and violates the first principle in the similarity weighting. Lewis's vision of the best system of analysis argues a law must have a good balance between ‘simplicity, strength, and fit’ (Lewis, 1994, pp480). First, simplicity in laws means it must avoid complexity which it can do by characterising laws with the smallest number of fundamental principles. Second, strength means the law must be able to successfully align with actual history, i.e. a law can predict a matter of fact such as two large objects of mass attracting each other.

Third, Lewis adds ‘fit’ with laws which means favouring some laws which fit or are closer to the ‘actual course of history … than others’(Lewis, 1994, pp480). For example, a system of laws is a better fit if its probability correlates with history. I might have one system of laws which 1), when rolling a die I will have a 0.5 chance of it landing odd and 0.5 chance of it landing even. I might also have another system of laws in which 2) if I roll a die I have a 0.1 chance of it landing odd and 0.9 chance of it landing even. Now in this world, if I roll the die 10 times and it only lands on an odd number once then the second system of laws is of better fit. Therefore, counterfactuals such as “If I had rolled it 20 times then I would have landed on an odd number 10 times” would be false since that would be a violation of law on the BSA.

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With Lewis’s BSA in place, we can now assess the indeterministic future similarity objection with Fines counterfactual. In the Nixon example, we have a 0.001 chance that there is a complete cover-up of all the consequences after Nixon presses the button. Consequently, a world that when Nixon presses the button leads to a complete cover-up is less similar to our world since such a world seems to have a law which gives the chances of a cover-up much higher. If Nixon presses the button and there is a complete cover-up then this would be a type of law violation since, on the BSA, a higher probabilistic law is less fitting with our world. A world where Nixon presses the button and there is a complete cover-up is less fitting since it seems the probability in such a world would be 1 as every example of Nixon pressing the button leads to a coverup. As a result, Fines counterfactual is still true on an indeterministic world since if the consequent is false this would be a wise spread violation of laws.

 

Objections against BSA
Although I believe the best system of analysis is the strongest defence against the indeterministic universe objection, there are reasons to suggest a complete coverup is not a violation of law. If Nixon pressed the button once and a complete cover-up occurred, it could be possible that it was a fluke and so could be compatible with the same probabilistic laws and fit of our world. For example, if there was a cover-up but Nixon pressed the button another 999 times without a complete cover-up then there is not a law violation as the probability fits with our world and the 0.001 probabilistic law we gave it.

Furthermore, the BSA is assessed over ‘all of history, past and present and future’ (Lewis, 1994, pp474). Therefore, any counterfactuals which are restrained to one occasion will always be compatible with being a possible but improbable event with probabilistic laws. This is because a single event could be probable when compared to all future events. For example, a counterfactual such as if ‘I drop this ball then it will bounce could have a law which gives it a 0.999 chance of occurring. Now suppose I drop it and it doesn’t bounce. This world would still be similar to our world and laws if the next 999 times it bounces. Likewise, if after 1000 drops it always bounces then it would be less similar and a violation of law on the BSA. Consequently, the BAS has not necessarily shown a law violation with the Nixon counterfactual.

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Moreover, supposing that the BSA could show a possible world with laws where Nixon presses the button leads to a cover-up is less fitting and a violation of law. There are several arguments against the BSA.

The best argument is presented by John Carroll with his Mirror argument (Lee, 2022, pp1015). Imagine a possible world ‘U1’ with five x particles and five y fields. Four of the x particles each travel through one of the four y fields and gain the property of spin up. One of the x particles, x5, travels past a mirror and through one of the untraveled y fields and becomes spin-up. Now imagine a possible world ‘U2’ which is like ‘U1’ except when the x5 particle travels past the mirror through a y field it does not gain a new property of spin up. Following the best system of analysis of laws we can propose a Law that “all x particles travelling through y fields will have a spin-up property”. The law is true in U1 and false in U2. However, now imagine a new set of possible worlds U1* and U2* where the mirror is moved down and blocks particle x5. Particle x5 never travels through y field and so will never be subjected to any changes it might or might not have had. Therefore, following the best system of analysis, the proposed Law is true in both U1* and U2* since in every case in history where the x particles travel through the y field it gains a spin-up property. From this, Carrol proposes a principle that if a state of affairs is physically possible and a law does not hold in that state, then even if that state doesn’t occur, the law does not hold (Lee, 2022, pp1014).

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Beebee presents an objection that we cannot presuppose that the laws would be the same in U2* than in U2 because it is not confirmed (Lee, 2022, pp1015). However, Carrols principle does show the counterintuitive nature of the BSA. It seems that Laws could be true by fluke events. If the mirror was moved slightly the laws could be different but since the mirror blocks the ability to verify a particular fact then it does not hold. This counterintuitive criterion for laws is a weakness of the BSA. This argument combined with the objections above presents a strong argument against Lewis’s account as he is unable to demonstrate a law violation or the truth of the Nixon example.

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Conclusion
In conclusion, we have presented Lewis's analysis of counterfactuals and a similarity weighting which successfully captures the truth condition of Fine’s counterfactual. Second, we then assess the hardest version of the future similarity objection with indeterminism. Following this we assessed two of the strongest rebuttals against the indeterministic world and demonstrated both fall short of providing a successful defence. Quasi-miracles are unconvincing. The BSA doesn’t seem to show a law violation and even if it did, we have reason to reject the BSA. Consequently, I do not believe Lewis provides a defensible account of counterfactuals.

 

 

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